We consider a service provider facing a continuum of delay-sensitive
strategic customers. The service provider maximizes revenue by charging
customers for the privilege of joining an M/G/1 queue and assigning them
service priorities. Each customer has a valuation for the service, with
a waiting cost per unit time that is proportional to their valuation;
customer types are drawn from a continuous distribution and are unobservable
to the service provider. We illustrate how to find revenue-maximizing
incentive-compatible priority pricing menus, where the firm charges higher
prices for higher queueing priority. We show that our proposed priority
pricing scheme is optimal across all incentive-compatible pricing policies
whenever the customer valuation distribution is regular. We compute the
resulting price menus and priority allocations in closed form when
customer
valuations are drawn from Exponential, Uniform, or Pareto distributions. We
find revenues in closed form for the special case of the M/M/1 queue, and
compute revenues in the more general setting numerically. We compare our
priority pricing scheme to the best fixed pricing scheme, as well as an
idealized pricing scheme where customers always reveal their valuation. We
observe the impact of service requirement variability on revenue and prices.
We also illustrate how to create the optimal discrete priority pricing
menu when the service provider is restricted to offering a
finite number of priority classes.

35 pages

*Tepper School of Business, Carnegie Mellon University
**Microsoft Research